Question: Simplify the expression. $(-7q^{3}+7q^{2}-2q)(-5q^{4}+7q^{2})$
Explanation: First use the distributive property. $ - 7 q^3 (-5 q^4) - 7 q^3 (7 q^2) + 7 q^2 (-5 q^4) + 7 q^2 (7 q^2) - 2 q (-5 q^4) - 2 q (7 q^2) $ Simplify. $ 35q^{7} - 49q^{5} - 35q^{6} + 49q^{4} + 10q^{5} - 14q^{3} $ $35q^{7}-35q^{6}-39q^{5}+49q^{4}-14q^{3}$ Identify like terms. $ { 35q^{7}} {- 49q^{5}} {- 35q^{6}} {+ 49q^{4}} {+ 10q^{5}} {- 14q^{3}} $ Add the coefficients. $ { 35q^{7}} { -35q^{6}} { -39q^{5}} {+ 49q^{4}} { -14q^{3}} $